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The intensity of radio recombination lines is very sensitive to departures from thermodynamic equilibrium. The populations of highly excited levels in the recombined atoms must be calculated from theory. Rates for processes that depopulate a level must be balanced by processes that repopulate the level, for a large set of levels, in the presence of boundary conditions at large and small principal quantum numbers $n$. Recent work (Hummer \&{} Mihalas 1988), well known in the field of stellar atmospheres, guides us to a different boundary condition at large $n$. The resulting, revised departure coefficients, when applied to the interpretation of the low frequency carbon recombination lines observed towards Cas~A, yield a sensible set of physical parameters for the line emitting region. In contrast, the unrevised departure coefficients would imply a line emitting region far from thermal balance and out of pressure balance with the ISM. The interpretation of recombination lines from H{\sc ii} regions and the diffuse ISM will also require revision.
